what are some (two) dangers of majority rule (using evidence from Madison and other federalist papers and founding documents)

The correct answer is:

It would lead to tyranny, it would deprive the minority of their rights.

Explanation:

The principal danger of majority rule according to the Founding Fathers of the United States is that if the majority of a government is composed by people with the same ideals and commitments it would lead to tyranny and there would be little tolerance for any who disagreed.

James Madison refers to this danger in the Federalist essay No. 10, and also talks about the necessary evil of factions, and how factions would prevent majority rule leading to tyranny because of the diversity of opinions.

The second danger of a majority rule according to the Federalist essay No. 51 is that if a majority is united by a common interest, the rights of the minority would be deprived. If the majority elects representatives willing to pass laws that only benefit that majority, the minority's rights would be compromised.

The separation of powers, the system of checks and balances and the Bill of Rights prevent this two dangers.